A column is filled with an organic peat moss $($density $600$ kg$/$m$3).$ The column has a circular

cross section, with a diameter of $1\mathrm{.}5$ meters and a length of $3$ meters. Flow is applied to the

column at a rate of $250$ L$/$m$2*$min$.$ The influence concentration of a carcinogenic chemical is $4$

mg$/$L$.$ The effluent cannot exceed $0\mathrm{.}5$ mg$/$L$.$ Assume a Fruendlich sorption isotherm relationship,

with Kf $=0\mathrm{.}762,$ N $=3\mathrm{.}558.$ Q $=$ flow rate $*$ cross$-$sectional area.

$($a$)$ How long can this column treat water without the effluent exceeding $0\mathrm{.}5$ mg$/$L$?$

$($b$)$ How much water will be treated over the duration?